Related papers: Trace decategorification of the Hecke category

We provide a dual version of the Geck--Rouquier Theorem on the center of an Iwahori--Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank $2$, for which the symmetrising trace conjecture is…

Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical…

Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these…

Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations when W is a right-angled Coxeter group.

In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. As another application of these descent theoretic methods, we compute the cellular Picard…

Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti Geometric Langlands Conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem…

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology…

The Dedekind zeta function of a quadratic number field factors as a product of the Riemann zeta function and the $L$-function of a quadratic Dirichlet character. We categorify this formula using objective linear algebra in the abstract…

The evaluation of cell tracking results steers the development of tracking methods, significantly impacting biomedical research. This is quantitatively achieved by means of evaluation metrics. Unfortunately, current metrics favor local…

We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e. without appealing to the classification…

We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The…

We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track…

We propose a simplified definition of Quillen's fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept of action. This advantage arises from the understanding…

We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to…

Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline…

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…

A pretorsion theory for the category of all categories is presented. The associated prekernels and precokernels are calculated for every functor.

We describe an approach to express the geometric side of the Arthur-Selberg trace formula in terms of zeta integrals attached to prehomogeneous vector spaces. This will provide explicit formulas for weighted orbital integrals and for the…

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…